DLMF:9.11.E4

MaRDI QIDQ3609

• Label: DLMF:9.11.E4

Digital Library of Mathematical Functions ID 9.11.E4

${\displaystyle{\displaystyle{\mathrm{Ai}^{2}}\left(z\right)+{\mathrm{Bi}^{2}}\left(z\right)=\frac{1}{\pi^{3/2}}\int_{0}^{\infty}\exp\left(zt-\tfrac{1}{12}t^{3}\right)t^{-1/2}\mathrm{d}t.}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}$:
• ${\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\exp\NVar{z}}}$: exponential function
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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